Details:
Title  The regularity of Tor and graded Betti numbers.  Author(s)  David Eisenbud, Craig Huneke, Bernd Ulrich  Type  Article in Journal  Abstract  Let S = K[x1, . . . , xn], let A, B be finitely generated graded Smodules, and let m = (x1, . . . , xn) ⊂ S. We give bounds for the regularity of the local cohomology of Tork (A, B) in terms of the graded Betti numbers of A and B, under the assumption that dim Tor1 (A, B) ≤ 1. We apply the results to syzygies, Gröbner bases, products and powers of ideals, and to the relationship of the Rees and symmetric algebras. For example we show that any homogeneous linearly presented mprimary ideal has some power equal to a power of m; and if the first [(n  1)/2] steps of the resolution of I are linear, then I2 is a power of m.  ISSN  00029327; 10806377/e 
URL 
http://muse.jhu.edu/login?auth=0&type=summary&url=/journals/american_journal_of_mathematics/v128/128.3eisenbud.pdf 
Language  English  Journal  Am. J. Math.  Volume  128  Number  3  Pages  573605  Publisher  Johns Hopkins University Press, Baltimore, MD  Year  2006  Edition  0  Translation 
No  Refereed 
No 
